"""Create an educational video to explain the CFA Level 1 knowledge: location measures (e.g., percentiles) 🎓 Content Requirements: Start with a clear, beginner-friendly definition of the concept Explain the core components and logic step by step Include simple numerical examples or visual analogies Add a short summary or key takeaways at the end Ensure the structure follows a logical teaching flow from concept to application 🎨 Visual and Layout Requirements: Full-screen visuals with centered, readable content Use smooth animations to transition between steps or sections Highlight important terms, formulas, and keywords with bright accent colors (e.g., yellow, red, blue) Avoid text crowding or overlap; leave clear visual spacing Use animated icons, graphs, or diagrams where appropriate (e.g., timelines, flowcharts, charts) Minimize blank space; keep each screen visually rich and balanced 🗣️ Tone and Style: Friendly, clear, and professional Focus on making the topic accessible for first-time learners Avoid excessive jargon; use plain language wherever possible Maintain alignment with CFA curriculum terminology and scope"""

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Welcome to our lesson on location measures, specifically percentiles. Location measures are statistical tools that help us understand where data points sit within a distribution. Percentiles are one of the most important location measures used in statistics and finance. A percentile tells us the percentage of observations that fall below a specific value. For example, the 75th percentile means that 75% of all data points are below this value, while 25% are above it. This concept is fundamental for understanding data distribution and making informed financial decisions. Now let's learn how to calculate percentiles step by step. First, we order our data from smallest to largest. Next, we calculate the position using the formula: Position equals P over 100, times n plus 1, where P is the percentile we want and n is the number of values. For the 75th percentile with 10 data points, this gives us position 8.25. Since this isn't a whole number, we interpolate between the 8th and 9th values. The 8th value is 35 and the 9th is 38. We take 35 plus 0.25 times the difference, giving us 35.75 as our 75th percentile. Let's work through a practical example using portfolio returns. We have monthly returns from the past year, ranging from negative 2.1% to positive 5.5%. To find the 25th percentile, we calculate the position as 25 over 100, times 12 plus 1, which equals 3.25. Since this falls between the 3rd and 4th values, we interpolate between 0.5% and 1.2%. Taking 0.5% plus 0.25 times the difference gives us 0.675%. This means that 25% of months had returns below 0.675%, making this our first quartile. Percentiles are closely related to other important location measures. Quartiles divide data into four equal parts: Q1 is the 25th percentile, Q2 is the 50th percentile which is also the median, and Q3 is the 75th percentile. The interquartile range, or IQR, is calculated as Q3 minus Q1 and measures the spread of the middle 50% of data. Deciles divide data into ten equal parts, representing the 10th, 20th, 30th percentiles and so on up to the 90th percentile. These measures are fundamental tools in financial analysis for understanding risk and return distributions. Let's summarize the key takeaways about location measures and percentiles. Percentiles show the relative position of data points within a distribution. Remember the formula: Position equals P over 100, times n plus 1. When the position has decimals, always interpolate between the nearest values. These concepts are essential for CFA Level 1, particularly in portfolio performance analysis, risk management including VaR calculations, benchmark comparisons, and client reporting. Common percentiles include the 25th, 50th, and 75th percentiles for quartile analysis, and the 95th and 99th percentiles for risk thresholds. Master these location measures to succeed in your CFA studies and professional finance career.